Singular spectrum analysis (SSA) is an advanced technique for signal processing, incorporating the elements of classical time series analysis, linear algebra, multivariate statistics, and dynamical systems. SSA aims to decompose a signal into the sum of a number of components with physical interpretation, such as a slowly varying trend, oscillatory components, and the noise. Based on these components, different algorithms for de-noising, change-point detection, missing data interpolation, synchronization detection, feature extraction, and prediction have been developed. For filtering out noise, in this method, the eigenvalues of the lagged covariance matrix is first obtained and arranged in a monotonically decreasing order. From a certain order, these eigenvalues may form a relatively planar tailing plane, i.e., so-called “noise floor”. The elementary components associated with larger eigenvalues on the initial steep portion of the singular spectrum are retained to form the basis of the signal subspace, while the components associated with the eigenvalues on the noise floor are discarded as the white noise. High eigenvalues corresponds to the fundamental oscillations in the signal, and the largest singular value is typically associated with slow-moving trend. This approach for truncated singular spectrum has been broadly used to de-noise speech, ultrasound, Doppler radar signals, biomedical (Electroencephalogram (EEG), Electrocardiogram (ECG) and Electromyography (EMG)) and mechanical signals, and hyperspectral image. In order to achieve satisfactory de-noising results, previous studies and inventions have focused on determining or finding the optimal order of a noise floor.
The original idea of the approach for truncated SSA is that there should be a ‘noise floor’ inherent in any signal, however, for many signals with lower signal-to-noise ratio (SNR), the singular spectrum has a smooth power-law form without a clear noise floor. In addition, the SSA algorithm itself only solves the representation problem of determining the best low-rank of the signal-plus-noise measurement matrix, however it says nothing about how to obtain a best estimate of the low-rank signal matrix. Therefore, one cannot expect such SSA de-noising approach to exhibit the optimal performance. In contrast, the singular spectrum employs a binary approach of retaining some components while discarding the other components. This is equivalent to filtering out the high frequency components of the signal, which fails to significantly improve the signal-to-noise ratio.
Fuzzy entropy (FuzzyEn) is a chaotic invariant used to characterize system complexity in chaos theory, and we herein introduce the concept of fuzzy entropy spectrum, with which a noise floor of the signal is represented. Depending on FuzzyEn noise spectrum of noisy signals, the invention proposes an iterative SSA threshold de-noising method.
It is an object of the present invention to, aiming at the shortcomings and disadvantages of the prior art as mentioned above, provide a fuzzy entropy based noisy signal processing method and an iterative singular spectrum analysis soft threshold de-noising method.